Robust reliable control in vibration suppression of sandwich circular plates

Abstract

The wide real life applications of circular plates under dynamic loading such as laminate saw blades and accurate slitting narrow industrial cutters require special attention to smart structural design that optimally handles the dynamic behavior of these configurations. The purpose of this paper is to investigate the vibration regulation of a sandwich circular plate using a non-fragile robust control strategy. A new dynamic modeling of the piezolaminated structure is proposed based on satisfying the Maxwell static electricity equation and on assuring the full coupling effects of the piezoelectric layers on the host structure. The Eigen functions are chosen optimally such that the boundary conditions for the piezoelectric sensor/actuator are satisfied without additional complexities. In order to reach to the desired performance in vibration attenuation, a robust controller is designed by considering the uncertainties that exist in the system matrices and controller itself. The proposed controller is obtained by solving a system of linear matrix inequalities (LMIs) that are based on the Bounded Real Lemma (BRL). Simulations show that the controller is capable of suppressing the vibration in existence of both the structured uncertainty in the system matrices and the feedback controller gain.